What is the circumference of a circle (to the nearest whole number) whose diameter is 12?

a) The velocity function is v(t) = -3 cos(t) - 1.

b) The object's displacement is 3sin(3) - K - 3.

c) The total distance traveled by the object from time 0 to time 3 is 3sin(3) + 3 meters.

a) To find the equation for the velocity of the object, we need to integrate the function for acceleration with respect to time. The velocity function v(t) is the antiderivative of a(t). Since a(t) = 3 sin(t), the antiderivative of a(t) is v(t) = -3 cos(t) + C, where C is the constant of integration.

We can find C using the initial velocity given. Since v(0) = -2m/s, we substitute t=0 and v(0) = -2m/s into the velocity function to get:

v(0) = -3 cos(0) + C = -2

Solving for C, we get C = -1. Now we can write the velocity function as:

v(t) = -3 cos(t) - 1

b) To find the displacement of the object from time 0 to time 3, we need to integrate the velocity function with respect to time over the interval [0,3]. The displacement function s(t) is the antiderivative of v(t):

s(t) = ∫v(t) dt = ∫(-3cos(t) - 1) dt = 3sin(t) - t - K

where K is the constant of integration. Since we want to find the displacement from time 0 to time 3, we evaluate s(3) - s(0):

s(3) - s(0) = (3sin(3) - 3) - (0 - K) = 3sin(3) - K - 3

c) To find the total distance traveled by the object from time 0 to time 3, we need to calculate the area under the absolute value of the velocity curve over the interval [0,3]. Since the velocity is negative for some time intervals, we take the absolute value of the velocity function:

|v(t)| = |-3cos(t) - 1| = 3cos(t) + 1

We can integrate this function from 0 to 3 to get the total distance traveled:

∫|v(t)| dt = ∫(3cos(t) + 1) dt = 3sin(t) + t + C

Evaluating this at t=3 and t=0, we get:

∫|v(t)| dt = (3sin(3) + 3) - (0 + 0) = 3sin(3) + 3

To learn more about function click on,

https://brainly.com/question/28875933

#SPJ1

Answer:

49

Step-by-step explanation:

[tex]\int\limits^{12}_0 {-0.002t^{2} +0.7t} \, dt \\=(-0.002\frac{{12}^{3} }{3} )+(0.7\frac{{12}^{2} }{2} )\\-(-0.002\frac{{0}^{3} }{3} )-(0.7\frac{{0}^{2} }{2} )\\\\=(-0.002\frac{{12}^{3} }{3} )+(0.7\frac{{12}^{2} }{2} )-0-0\\\\=49.248\\[/tex]

The method can be used to find the range of a set of data is Find the difference between the maximum and minimum values. Option A

The range of a given set of data can simply be defined as  the difference that exists between the lowest and highest values of the data.

This is done irrespective of the arrangement of data like in ascending or descending order.

The range of values can be misleading sometimes when there are extremely high or low values.

For a range of function, it is the mean value of all the outputs of that function.

Learn more about range at: https://brainly.com/question/24326172

#SPJ1

The annual insurance premium for John Noel and his wife is $616, which corresponds to option (b).

The annual insurance premium can be calculated using the following formula:

Annual premium = (Amount of insurance coverage / $100) x Rate per $100 of insurance

The amount of insurance coverage is 80% of the replacement value of the home, which is $250,000, so it is:

Amount of insurance coverage = 0.8 x $250,000 = $200,000

The rate per $100 of insurance depends on the fire protection class of the home. According to industry standards, fire protection class 5 has a rate of $0.308 per $100 of insurance.

Therefore, the rate per $1 of insurance is:

Rate per $1 of insurance = $0.308 / 100 = $0.00308

The rate per $100 of insurance is:

Rate per $100 of insurance = $0.00308 x 100 = $0.308

Using the formula above, we can calculate the annual insurance premium:

Annual premium = ($200,000 / $100) x $0.308 = $616

Therefore, the annual insurance premium for John Noel and his wife is $616, which corresponds to option (b).

Learn more about Insurance Premium:

https://brainly.com/question/19396263

#SPJ1

Answer: 4

Step-by-step explanation: because he needs to divided by 2

The sum of the geometric series is -12,276.

So, the correct answer is C. -12,276.

To find the sum of the geometric series, we can use the formula:

[tex]S = a \times (1 - r^n) / (1 - r),[/tex]

where S is the sum of the series,

a is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the first term (a) is 6(2) = 12, the common ratio (r) is 2, and the number of terms (n) is 10.

Plugging these values into the formula, we get:

[tex]S = 12 \times (1 - 2^{10} ) / (1 - 2).[/tex]

Calculating further:

[tex]S = 12 \times (1 - 1024) / (-1) = 12 \times 1023 = 12276.[/tex]

Therefore, the sum of the geometric series is -12,276.

So, the correct answer is C. -12,276.

For similar question on geometric series.

https://brainly.com/question/24643676

#SPJ11

The volume of the pyramid is 936 mi³

A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.

The volume of a pyramid is expressed as;

V = 1/3bh

where b is the base area and h is the height of the pyramid.

Area of the hexagon = 1/2 × p × a

perimeter = 6 × 6 = 36 mi

area = 1/2 × p × a

= 1/2 × 36 × 5.2

= 187.2/2

= 93.6 mi²

Volume = 93.6 × 10

= 936 mi³

therefore the volume of the pyramid is 936 mi³

learn more about volume of pyramid from

https://brainly.com/question/218706

#SPJ1

The surface area of the cube of side x-4 in terms of x is 6x² - 48x + 96.

Given length of a side of a cube (a) = x-4

The formula for finding the surface area of a cube = 6a²

By, substituting the 'a' value in the above formula we can obtain the surface area of the cube.

6a² = 6 * (x-4)²                           [a = x-4]

      = 6 * (x² - 8x + 16)

      = 6x² - 48x + 96

From the above analysis, we can conclude that the surface area of the given cube in terms of 'x' is 6x² - 48x + 96.

To know more about cube,

https://brainly.com/question/28776132

Answer:

When n is greater than 1/2 or always true

n > 1/2

Step-by-step explanation:

Rewrite.

0+0+6(n−1)=2(n+1)

Simplify by adding zeros.

6(n−1)=2(n+1)

Apply the distributive property.

6n+6⋅−1=2(n+1)

Multiply 6 by −1.6n−6=2(n+1)

Simplify 2(n+1).

6n−6=2n+2

Move all terms containing n to the left side of the equation.

4n−6=2

Move all terms not containing n to the right side of the equation.

4n=8

Divide each term in 4n=8 by 4 and simplify.

n=2

Answer:

62 degrees

Step-by-step explanation:

Hope this helps! If it’s wrong I’m really sorry. I used the formula θ = s/r then converted it from radians to degrees.
Pls give brainliest!

Answer:

So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.

Step-by-step explanation:

Let's assume that the length of one side of the square base of the box is "x". Then the height of the box is also "x" to maximize the volume.

The surface area of the box (excluding the top) is given by:

2(x^2) + 4(x^2) = 6(x^2)

The surface area of the metal top is:

x^2

The total surface area of the box is the sum of the surface area of the box and the surface area of the metal top:

6(x^2) + x^2 = 7(x^2)

The cost of the wood for the box is:

5 cents per square inch * 6(x^2) = 30x^2 cents

The cost of the metal for the top is:

12 cents per square inch * x^2 = 12x^2 cents

The total cost of the box is:

30x^2 + 12x^2 = 42x^2 cents

We want to find the maximum volume of the box that can be made with $30, which is 3000 cents. Therefore, we can set up the equation:

42x^2 = 3000

Solving for x, we get:

x^2 = 71.429

x ≈ 8.445

Therefore, the maximum volume of the box is:

V = x^2 * x = (8.445)^3 ≈ 606.526 cubic inches.

So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.

The domain of the relation, given the points the coordinate plane has, is A.{−5, −3, 0, 2, 5}

The range of representable x-values in a function or relation when plotted on a coordinate plane are regarded as the domain. This values serve as inputs that can generate correspondig outputs within functions and relations. Displayed along the x-axis, domains strictly adhere to their input-based designation.

The x values from the graph are, - 5, - 3, 0, 2, 5 .

This means that the domain is {−5, −3, 0, 2, 5}.

Find out more on domain at https://brainly.com/question/29630155

#SPJ1

Answer: -161

Step-by-step explanation: you solve by plugging 9 in for x so you get f(9) = -2(9)^2 +9-8 you solve using PEMDAS and you get -161

A recursive sequence are -20, -80, -320 and  -1280.

To write a recursive sequence that represents the sequence defined by the given explicit formula, we need to find a rule that relates each term of the sequence to the previous term.

The explicit formula for the sequence is

[tex]a_{n}[/tex] = -5 [tex](4)^{n-1}[/tex]

To find the recursive formula, we need to express each term in terms of the previous term. Let's say the first term of the sequence is  [tex]a_{1[/tex].

[tex]a_{1[/tex]  = -5 * 1 = -5

[tex]a_{2}[/tex] = -5 * 4 = -20

[tex]a_{3}[/tex] = -5 * 16 = -80

...

[tex]a_{n}[/tex] = -5 [tex](4)^{n-1}[/tex]

We can see that each term in the sequence is 4 times the previous term, so we can express the nth term in terms of the (n-1)th term as follows

[tex]a_{1[/tex] = -5

[tex]a_{n}[/tex] =  4[tex]a_{n-1}[/tex] , for n > 1

This gives us the recursive formula for the sequence. To generate the sequence, we start with the initial term [tex]a_{1[/tex] =-5 and use the recursive formula to find the subsequent terms.

For example, if we want to find a5, we can use the recursive formula

[tex]a_{2}[/tex] = 4[tex]a_{1[/tex] = 4(-5) = -20

[tex]a_{3}[/tex] =  4[tex]a_{2}[/tex] = 4(-20) = -80

[tex]a_{4}[/tex] = 4[tex]a_{3}[/tex] = 4(-80) = -320

[tex]a_{5}[/tex] = 4[tex]a_{4}[/tex] = 4(-320) = -1280

Therefore, [tex]a_{5}[/tex] = -1280.

To know more about recursive sequence here

https://brainly.com/question/12851933

#SPJ1

The answer choice which gives the best-example of the "random-sample" is (c) Ask 10 people from each "grade-level" at Allison's school about how many games they have on their phones.

A "Random-Sample" is a subset of a larger population which is chosen in such a way that each member of the population has an equal chance of being selected.

The Option (c) :  gives the best example of a random sample that Allison could use to help answer her question. By asking 10 people from each grade level at her school, Allison can obtain a sample that includes a variety of ages, genders, and backgrounds.

This can help to ensure that the sample is representative of the population she is interested in studying.

Option (a) : is not a random sample because it only includes teenagers who happen to be at the grocery store at the time Allison is conducting her survey. This may not represent entire population of teenagers at her school.

Option (b) : is not a random sample either because it only includes people who happen to be at the library on Saturday morning. This may not be representative of the entire population of teenagers at her school.

Option (d) :  is not a random sample because it only includes teenagers from 20 different countries. This may not be representative of the population of teenagers at Allison's school or in her local area.

Therefore, the correct option is (c).

Learn more about Random Sample here

https://brainly.com/question/461539

#SPJ1

Answer:

Step-by-step explanation:

Add '-1.25' to each side of the equation.

1.25 + -1.25 + -0.5x = 0.75 + -1.25 + 3.5n

Combine like terms: 1.25 + -1.25 = 0.00

0.00 + -0.5x = 0.75 + -1.25 + 3.5n

-0.5x = 0.75 + -1.25 + 3.5n

Combine like terms: 0.75 + -1.25 = -0.5

-0.5x = -0.5 + 3.5n

Divide each side by '-0.5'.

x = 1 + -7n

Simplifying

x = 1 + -7n

The item is an inelastic good at a price of 6 because it is negative and have a demand of -0.71.

The formula for elasticity of demand is Elasticity of demand = (% change in quantity demanded) / (% change in price)

The initial quantity demanded at a price of 6 and the quantity demanded at a slightly different price must be know.

Let say Initial quantity demanded is:

x = -0.7(6) + 10

x = 5.8

Assume price changes slightly to 6.01, which gives us a new quantity demanded of x:

= -0.7(6.01) + 10

= 5.793

The % change in quantity demanded will be:

= [(new quantity demanded - initial quantity demanded) / initial quantity demanded] x 100%

= [(5.793 - 5.8) / 5.8] x 100%

= -0.12%

As price has changed from 6 to 6.01, we can calculate the percentage change as follows:

% change in price = [(new price - initial price) / initial price] x 100%

= [(6.01 - 6) / 6] x 100%

= 0.17%

Elasticity of demand = (% change in quantity demanded) / (% change in price)

= (-0.12% / 0.17%)

= -0.71

Read more about demand elasticity

brainly.com/question/29615048

#SPJ1

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

B. y=5

Step-by-step explanation:

3y-4<11

3y-4+4<11+4

3y<15

3y/3<15/3

y<5

The effect of the transformation is a vertical srhink of scale factor 1/9.

For a function f(x), can define a vertical dilation of scale factor k as:

g(x) = k*f(x).

In this case the transformation is:

f(x) ---> (1/9)*f(x)

So we have a vertical dilation of scale factor k = 1/9, so we have a vertical contraction.

Then the effect that this will have in the graph is that it will contract/shrink it vertically.

Learn more about transformations at:;

https://brainly.com/question/4289712

#SPJ1

Answer:

The greatest area enclosed by the fence will be a square. If the farmer has 60 metres of perimeter fencing, he can use 15 meters of fencing for each side of the square. This would give him an area of 15² = 225 m². Since he can keep one chicken for every square meter, he can keep 225 chickens. Therefore, the farmer should arrange his fence in the shape of a square to get the greatest area.

Answer:

To determine the domain of f - g, we need to first find the expression for f - g.

f - g = (x^2 - 4) - (2x + 3)

f - g = x^2 - 2x - 7

The domain of f - g is the set of all real numbers for which the expression x^2 - 2x - 7 is defined.

We know that a quadratic expression of the form ax^2 + bx + c is defined for all real numbers x, so long as the expression under the square root in the quadratic formula (b^2 - 4ac) is non-negative.

In this case, a = 1, b = -2, and c = -7, so the expression under the square root is:

b^2 - 4ac = (-2)^2 - 4(1)(-7) = 4 + 28 = 32

Since 32 is positive, we know that the expression x^2 - 2x - 7 is defined for all real numbers x, and therefore the domain of f - g is all real numbers.

So the answer is not among the choices given.

The scale factor will be one-third which is 1/3. Then the correct option is A.

Given that:

Dimension of a small triangle, 6, 8, and 10

Dimension of a giant triangle, 18, 24, and 30

Dilation is the process of increasing the size of an item without affecting its form. The object's size can be raised or lowered depending on the scale factor. There is no effect of dilation on the angle.

The scale factor is calculated as,

SF = 6 / 18

SF = 1 / 3

The scale factor will be one-third which is 1/3. Then the correct option is A.

More about the dilation link is given below.

https://brainly.com/question/2856466

#SPJ1

Answer:

1/3

Step-by-step explanation:

I took the test!

Answer:

[tex]y - 4 = - 3(x - 2)[/tex]

Answer: 599.7 square miles

Step-by-step explanation: Divide 2,099,451 by 3501 and then round to the nearest tenth.

a) 18 Kids own their own instruments.

b) 72 kids rent instruments.

c) 80%  percentage of the kids rent their instruments.

We have,

There are 90 kids in the band.

20% of the kids own their own instruments.

a. How many kids own their own instruments?

So, 20% of 90

= 20/100 x 90

= 1/5 x 90

= 18 kids

b. How many kids rent instruments?

= 90 - 18

= 72 Kids

c. . What percentage of the kids rent their instruments?

So, x% of 90 = 72

90x = 7200

x= 80%

Learn more about Percentage here:

https://brainly.com/question/29306119

#SPJ1

Answer:

Beauty algebra is not a recognized term or concept within the field of mathematics. Therefore, there is no main idea associated with it in mathematical context. It is possible that the term is used in a different context or field, but without additional information, it is not possible to provide a more accurate answer.

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

To learn more about equation click on,

https://brainly.com/question/28049884

#SPJ1

The quadratic equation representing the new patio area after adding a decorative tile of width x all the way around is: 0 = 4x^2 + 44x - 60

Options A and E are correct.

In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.

Since the area of the new patio is given as 180 square feet, we can create a quadratic equation to represent the new patio area:

Area = length × width

180 = (12 + 2x) × (10 + 2x)

After we expand, the answer is given as 0 = 4x^2 + 44x - 60

Read more about quadratic equation here:

https://brainly.com/question/1214333

#SPJ1

The sinusoidal function that matches the specified graph, expressed using π ≈ 3.1416 is; y ≈ 4·sin(0.628·(x + 3))

A sinusoidal function is a periodic function that is based on either the sine or the cosine function.

The general form of a sinusoidal function is; y = A·cos(B·(x - C)) + D

The peak and the trough of the graph of the function indicates that the amplitude, A = (4 - (-4))/2 = 4

The vertical shift, D = (4 + (-4))/2 = 0

The period, P = 2·π/B

A cycle is completed in -0.5 - (-10.5) = 10 units of the x-value interval

P = 10 = 2·π/B

Therefore; B = π/5

When x = -8, y = 0, therefore;

0 = 4·sin((π/5)·((-8) - C)) + 0

4·sin((π/5)·((-8) - C)) = 0

sin((π/5)·((-8) - C)) = 0

(π/5)·((-8) - C) = 0

((-8) - C)  = 0

C = -8

When x = 2, y = 0, therefore;

0 = 4·sin((π/5)·(2 - C)) + 0

4·sin((π/5)·(2 - C)) = 0

sin((π/5)·(2 - C)) = 0

(π/5)·(2 - C) = 0

(2 - C)  = 0

C = 2

Similarly; When x = -3, y = 0, therefore; C = -3

y = 4·sin((π/5)·(x + 3))

The value C = -3, corresponds to the horizontal shift of the graph of the sine function, which is shifted 3 units to the left

The sinusoidal function, where π ≈ 3.1416 is therefore;

y ≈ 4·sin((0.628)·(x + 3))

Learn more on sinusoidal functions here: https://brainly.com/question/29529184

#SPJ1